Information on Result #613613
Linear OA(536, 3125, F5, 9) (dual of [3125, 3089, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 3124 = 55−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9
Mode: Constructive and linear.
Optimality
Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OA(540, 3131, F5, 9) (dual of [3131, 3091, 10]-code) | [i] | (u, u+v)-Construction | |
| 2 | Linear OA(541, 3136, F5, 9) (dual of [3136, 3095, 10]-code) | [i] | ||
| 3 | Linear OOA(536, 2636, F5, 2, 9) (dual of [(2636, 2), 5236, 10]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 4 | Linear OOA(536, 2636, F5, 3, 9) (dual of [(2636, 3), 7872, 10]-NRT-code) | [i] | ||
| 5 | Digital (27, 36, 2636)-net over F5 | [i] | ||
| 6 | Linear OA(542, 3131, F5, 11) (dual of [3131, 3089, 12]-code) | [i] | ✔ | Construction X with Extended Narrow-Sense BCH Codes |
| 7 | Linear OA(536, 3130, F5, 9) (dual of [3130, 3094, 10]-code) | [i] | ✔ | |
| 8 | Linear OA(549, 3138, F5, 12) (dual of [3138, 3089, 13]-code) | [i] | ✔ | |
| 9 | Linear OA(537, 3136, F5, 9) (dual of [3136, 3099, 10]-code) | [i] | ✔ | |
| 10 | Linear OA(555, 3144, F5, 13) (dual of [3144, 3089, 14]-code) | [i] | ✔ | |
| 11 | Linear OA(539, 3143, F5, 9) (dual of [3143, 3104, 10]-code) | [i] | ✔ | |
| 12 | Linear OA(563, 3151, F5, 14) (dual of [3151, 3088, 15]-code) | [i] | ✔ | |
| 13 | Linear OA(564, 3153, F5, 14) (dual of [3153, 3089, 15]-code) | [i] | ✔ | |
| 14 | Linear OA(562, 3151, F5, 14) (dual of [3151, 3089, 15]-code) | [i] | ✔ | |
| 15 | Linear OA(571, 3158, F5, 16) (dual of [3158, 3087, 17]-code) | [i] | ✔ | |
| 16 | Linear OA(569, 3158, F5, 15) (dual of [3158, 3089, 16]-code) | [i] | ✔ | |
| 17 | Linear OA(570, 3157, F5, 15) (dual of [3157, 3087, 16]-code) | [i] | ✔ | Construction XX with a Chain of Extended Narrow-Sense BCH Codes |
| 18 | Linear OA(568, 3154, F5, 15) (dual of [3154, 3086, 16]-code) | [i] | ✔ | |
| 19 | Linear OA(571, 3156, F5, 16) (dual of [3156, 3085, 17]-code) | [i] | ✔ | |
| 20 | Linear OA(562, 3148, F5, 14) (dual of [3148, 3086, 15]-code) | [i] | ✔ | |
| 21 | Linear OA(561, 3146, F5, 14) (dual of [3146, 3085, 15]-code) | [i] | ✔ | |
| 22 | Linear OA(565, 3155, F5, 14) (dual of [3155, 3090, 15]-code) | [i] | ✔ | |
| 23 | Linear OA(557, 3148, F5, 13) (dual of [3148, 3091, 14]-code) | [i] | ✔ | |
| 24 | Linear OA(556, 3146, F5, 13) (dual of [3146, 3090, 14]-code) | [i] | ✔ | |
| 25 | Linear OA(548, 3133, F5, 12) (dual of [3133, 3085, 13]-code) | [i] | ✔ | |
| 26 | Linear OA(543, 3133, F5, 11) (dual of [3133, 3090, 12]-code) | [i] | ✔ | |
| 27 | Linear OA(541, 3146, F5, 9) (dual of [3146, 3105, 10]-code) | [i] | ✔ | |
| 28 | Linear OA(570, 3156, F5, 16) (dual of [3156, 3086, 17]-code) | [i] | ✔ | |
| 29 | Linear OA(569, 3154, F5, 16) (dual of [3154, 3085, 17]-code) | [i] | ✔ | |
| 30 | Linear OA(537, 3137, F5, 9) (dual of [3137, 3100, 10]-code) | [i] | ✔ | Construction X4 with Extended Narrow-Sense BCH Codes |